One row wavelet sensor layout for resistivity imaging

Abstract

A sensor electrode for imaging a formation. The sensor includes a geometry either reduces or substantially limits spatial aliasing in formation data. The aliasing is the result of imaging the formation with an array of the sensor electrodes.

1. A method for designing a sensor electrode for incorporation in a resistivity imaging instrument, the sensor electrode for interrogating an earth formation, the method comprising:
 determining a geometry for the sensor electrode; 
 evaluating a response function for resistivity measurements collected with the sensor electrode; and 
 adjusting a geometry of the sensor electrode to improve the response function; 
 wherein determining comprises selecting dimensions for the sensor electrode such that in an array of the sensor electrodes, (1/apparent horizontal dimension of the sensor electrode) is less than (2/horizontal separation of each sensor electrode of the array). 
 
     
     
       2. The method as in  claim 1 , wherein the response function comprises a response function for at least one of spatial aliasing, spatial offset, angular dependence, frequency response and resolution. 
     
     
       3. The method as in  claim 1 , wherein the geometry for the sensor electrode is one of a diamond shape, a one-row zigzag shape, a one-row double zigzag shape, a one-row triple zigzag shape and a one-row wavelet shape. 
     
     
       4. A computer program product stored on machine readable media, the product comprising machine executable instructions for designing a sensor electrode for incorporation in a resistivity imaging instrument, the sensor electrode for interrogating an earth formation, the instructions comprising instructions for:
 receiving an input geometry for the sensor electrode; 
 evaluating at least one response function for the sensor electrode; and 
 adjusting the input geometry for the sensor electrode according to desired response for each response function to create an adjusted geometry. 
 
     
     
       5. The computer program product as in  claim 4 , wherein the response function comprises a Nyquist criteria.